This paper presents a novel Non-Intrusive Load Monitoring (NILM) approach focusing on the Energy Efficiency (EE) assessment of residential appliances. This approach (NILMEE) is able to identify the individual consumption of several household devices, providing proper information for evaluating energy efficiency and pointing out the operational issues or labelling mismatches of appliances, while recommending better practices for energy usage in specific consumer installations. The proposed approach was developed and evaluated by embedding the NILM engine on an electronic power meter, which performs a microscopic analysis on measured voltages and currents and provides the load disaggregation using the Conservative Power Theory for the feature extraction, K-Nearest Neighbours for the appliance classification, and the Power Signature Blob for the energy disaggregation. The disaggregation algorithm performance evaluation is carried out using NILMTK. Results show that NILM transcends the regular energy usage calculation, serving as a tool that enables the diagnosis of household appliances using the energy efficiency indexes provided by labels and standards.